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gptkbp:instanceOf
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gptkb:theoretical_computer_science
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gptkbp:alsoKnownAs
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gptkb:Exact_Cover
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gptkbp:application
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Polyomino packing
Sudoku solving
Tiling problems
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gptkbp:category
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gptkb:Theoretical_computer_science
gptkb:mathematical_optimization
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gptkbp:complexity
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NP-complete
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gptkbp:decision
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Does there exist a subcollection of subsets that covers each element exactly once?
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gptkbp:definedIn
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Given a universe and a collection of subsets, find a subcollection that partitions the universe
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gptkbp:firstDescribed
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gptkb:Donald_Knuth
1970s
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gptkbp:hasVariant
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gptkb:Exact_Cover_by_3-Sets_(X3C)
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gptkbp:input
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collection of subsets
universe of elements
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gptkbp:output
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subcollection of subsets
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gptkbp:outputCondition
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each element is covered exactly once
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gptkbp:reduces
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gptkb:3-SAT
gptkb:Exact_Cover_by_3-Sets_(X3C)
gptkb:Sudoku
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gptkbp:relatedTo
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gptkb:Set_Cover_Problem
gptkb:NP-complete_problem
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gptkbp:solvedBy
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gptkb:Algorithm_X
gptkb:Dancing_Links
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gptkbp:bfsParent
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gptkb:Karp's_21_NP-complete_problems
gptkb:Reducibility_Among_Combinatorial_Problems_(Karp,_1972)
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gptkbp:bfsLayer
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6
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https://www.w3.org/2000/01/rdf-schema#label
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Exact Set Cover
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